APPROXIMATING PROBABILISTIC INFERENCE IN BAYESIAN BELIEF NETWORKS

A belief network comprises a graphical representation of dependencies between variables of a domain and a set of conditional probabilities associated with each dependency. Unless P=NP, an efficient, exact algorithm does not exist to compute probabilistic inference in belief networks. Stochastic simulation methods, which often improve run times, provide an alternative to exact inference algorithms. We present such a stochastic simulation algorithm D-BNRAS that is a randomized approximation scheme. To analyze the run time, we parameterize belief networks by the dependence value D(xi), which is a measure of the cumulative strengths of the belief network dependencies given background evidence xi. This parameterization defines the class of f-dependence networks. The run time of D-BNRAS is polynomial when f is a polynomial function. Thus, the results of this paper prove the existence of a class of belief networks for which inference approximation is polynomial and, hence, provably faster than any exact algorithm.